Authors: Muhammad Suhail Shaikh, Gengzhong Zheng, Chang Wang, Chunwu Wang, Xiaoqing Dong, Konstantinos Zervoudakis
Categories: Article, Academic performance, Anxiety, Engineering, Improved mayfly clustering, Mathematics and computing, Optimization method, Psychological fitness, Psychology
Source: Scientific Reports
Anxiety is an important issue that affects their academic performance, mental health, and overall educational journey. To address this issue, it is important to accurately assess anxiety levels and provide evidence-based techniques. However, due to the complexity of anxiety and individual differences, analyzing clustering algorithms to efficiently classify psychological levels is challenging. Traditional clustering techniques face certain challenges in accurately classifying anxiety levels, such as slow convergence, sensitivity to initial conditions, and difficulties in handling constraints. To address these issues, clustering with an improved Mayfly-based optimization algorithm (IMOA) is proposed based on the dynamic variable for better performance to classify psychological levels. Initially, IMOA is validated using 23 standard benchmark functions, confirming its ability to find optimal solutions. Then, IMOA is applied to the student dataset, classifying them into Cluster A and Cluster B. The average scores for both clusters across all test cases are 76.7% and 53.07%, respectively. These results demonstrate the formation of dissimilar student groups with homogeneous emotions and performance, highlighting the importance of addressing emotional stress. Finally, by assigning students to clusters, educators and mental health professionals can better support those who may struggle, ensuring they receive the attention and resources they need. The obtained results show that IMOA with a dynamic variable effectively classifies student anxiety, improving the learning environment and helping teachers better understand students’ needs. This identification allows them to provide more effective support and adapt their teaching to meet the specific needs of those seeking support.
Keywords: Optimization method, Improved mayfly clustering, Psychological fitness, Anxiety, Academic performance
**Subject ** Psychology, Engineering, Mathematics and computing
Psychological effects refer to the feelings of uncertainty and anxiety experienced by students in an academic environment, impacting their ability to learn and perform well. These effects can appear in various forms, such as exam anxiety or social anxiety, and are influenced by some other factors like academic pressure, social challenges, technology use, financial concerns, and access to mental health resources. Anxiety and mental health issues have gained a lot of attention due to rising academic pressures, depression, social influences, financial stress, and increased awareness^1^. Educational institutions and mental health supporters are working to address these issues through different efforts such as counseling services, stress management programs, and reducing stigma^2,3^. However, student anxiety remains a significant concern, emphasizing the need for continued attention and support. Exam anxiety involves heightened stress during tests, leading to impaired performance. Social anxiety causes discomfort in social situations, preventing peer interactions and participation in academics. Performance anxiety results in excessive worry about meeting expectations, which leads to self-doubt and avoidance behaviors. Generalized anxiety involves constant worry about academic pressures, often with physical symptoms. This greatly affects academic performance, social relationships, health, and well-being. Early recognition and support are the main factors in helping students manage anxiety and succeed both academically and personally^4,5^. Addressing students mental health issues is a complex challenge that requires collaboration among various sectors of society, including educational institutions, healthcare providers, policymakers, community organizations, and public concern^6^. The existing research shows the relevant measures taken by each sector, drawing upon existing literature, and identifies the limitations associated with these measurements.
However, there are some limitations that each sector may face when implementing measures to address students’ mental health issues. Such as Educational institutions and healthcare systems often struggle with resource limitations, resulting in long wait times, inadequate staffing, and insufficient funding for mental health services^15^. Despite efforts to reduce stigma, many students still face barriers to seeking help, such as fear of judgment, confidentiality concerns, and lack of awareness. Additionally, there is fragmentation between mental health services, primary care providers, and educational institutions^16^. Furthermore, current measures primarily focus on treating students with existing mental health issues, there is a need for greater emphasis on prevention and early intervention strategies to address risk factors and promote mental well-being proactively^17^. Collaborative efforts from all sectors of society are essential for effectively addressing students’ mental health issues. However, measures such as counseling services, integrated care models, funding allocation, peer support groups, and mental health policies have been implemented, they are not without limitations. Overcoming challenges related to resource constraints, stigma, fragmented care systems, and the need for prevention-focused approaches is important for improving mental health outcomes among students. To address these limitations, the proposed study aimed to classify student anxiety levels. The main objective is to accurately assess the anxiety levels in students. This accurate classification will help policymakers in formulating targeted interventions to prevent associated problems and ensure that at-risk students receive the necessary support.
This section aims to review existing research on the significance of anxiety.
Traditional methods such as questionnaire surveys rely on counselors or psychological institutions for manual assessment of student anxiety levels. These methods classically involve the administration of standardized questionnaires or scales, which are then scored and analyzed by trained professionals to determine the intensity of anxiety symptoms in students^18^. This process often requires the expertise of psychologists who have the necessary training to accurately assess and diagnose anxiety disorders. While these methods have been widely used in research and clinical environments, they can be time-consuming and resource-intensive, requiring access to qualified personnel and specialized assessment tools. Additionally, manual assessment may introduce subjectivity and variability in the interpretation of results, potentially affecting the reliability and validity of findings^19,20^. In^21^ the author presented a comprehensive overview of machine learning segmentation techniques for anxiety disorders. However, the author in^22^ explores the applications of algorithms based on machine learning for the prediction of stress, anxiety, and depression in modern society. In^23^, the author proposed a human activity identification-based method to identify anxious behavior through the use of motion sensors. The author of^24^ suggested employing machine learning to analyze speech for indications of depression and anxiety in young children. In^25,26^, the authors present a method for dynamically tracking state anxiety using multi-modal data and machine learning. In this research study, author^27^ employed a Bayesian neural network that utilized a feature ensemble approach to predict anxiety disorders. Furthermore, the authors in^28,29^ consider different evaluation objectives to identify students with anxiety.
Clustering is the process of dividing a dataset into a set number of groups to maximize differences between groups while minimizing differences within groups. It is widely used in engineering and scientific fields, especially in data mining. The most common method, data clustering, is categorized into hierarchical and partitional clustering^30^. In this research, partitional clustering is adopted, where each cluster is represented by its centroid. Initially, each data object is assigned to the closest centroid, and then the centroids are updated based on the current assignment and by optimizing certain criteria^31^. Among partitional clustering algorithms, the k-means algorithm is the most popular and widely used technique. It is a fast and simple algorithm designed to minimize the average squared distance^32^. However, k-means efficiency heavily relies on the initial selection of cluster centers and is susceptible to convergence towards local optima. To minimize these issues, the k-means + + algorithm is introduced to improve the initial selection of centroids^33^. Despite this improvement, k-means + + still struggles to converge to local optima^34^. Then a fuzzy clustering algorithm has been recently proposed, but it faces limitations with large datasets^35^. Additionally, a fuzzy differential evolution algorithm is utilized for optimal product line design to address complex challenges^36^. Clustering with optimization techniques has attained more attention as an alternative to traditional clustering methods, indicating significant progress in data analysis techniques^37^. Different optimization techniques have been recently proposed to address these issues, but further advancements are still needed. However, with advancements in technology, there has been a growing interest in the application of improved optimization methods to enhance the accuracy and efficiency of anxiety assessment. These methods offer the potential for automated and objective assessment, which could overcome the limitations of traditional methods. Improved optimization algorithms are widely used and effective computational intelligence techniques for solving complex problems^38^. In the last few years, a group of optimization approaches^39,40^ known as metaheuristics algorithms has been developed to address limitations in optimization such as excessive mathematical calculations, initial conditions, and convergent issues^41^. As shown in Fig. 1, the optimization approaches are classified into four different groups^42,43^. The improved optimization methods represent a promising direction in the field of anxiety assessment, offering opportunities for more efficient, objective, and personalized evaluation of anxiety levels among students. The authors proposed IMOA due to the following advantages.
Fig. 1 Classification of optimization techniques.
The primary aim of this research is to examine student anxiety levels. Nowadays, there is a growing recognition of the importance of addressing mental health concerns, particularly among students. Anxiety has become a common and significant issue that impacts academic performance, well-being, and future success. To effectively support student mental health and promote a conducive learning environment, it is important to develop innovative approaches for assessing and addressing anxiety levels. Traditional methods of assessing student anxiety often rely on subjective self-report measures, which may lack precision and fail to capture the complexity of this multifaceted phenomenon. Moreover, existing optimization methods used in resource allocation for mental health programs may not fully utilize the potential for enhancing assessment processes and strategies customized to individual student needs.
Motivated by the need for more accurate and efficient student-centered methods to assess anxiety levels, the IMOA is proposed. Inspired by the unique mating behavior of mayflies, the IMOA provides a new framework for optimizing complex systems through iterative search and adaptation. By enhancing the traditional MOA with a dynamic variable, the goal is to create a model that can dynamically assess student anxiety levels. Unlike conventional optimization methods, which may miss the nonlinear and dynamic aspects of anxiety, the IMOA can adaptively explore the solution space, taking into account various factors affecting student well-being. This innovative approach establishes the IMOA as a promising method for understanding student anxiety and enhancing support systems that promote student well-being.
The following is the main contribution of this research work.
O1: Proposed an IMOA to classify student psychological levels.
O2: IMOA exhibited superior performance compared to various existing algorithms, including GWO^44^, MFO^45^, and WOA^46^, across 23 different benchmark functions, such as unimodal, multimodal, and high-dimensional multimodal functions. A detailed statistical analysis is conducted based on individual runs, and the proposed method’s consistency is validated using a boxplot.
O3: Comprehensive analysis and comparison of the results obtained from IMOA against different established algorithms, demonstrating that IMOA continually generates better results in terms of both reliability and effectiveness.
O4: The main objective of this study is to explore the classification of student anxiety. Additionally, the emotional states of students are categorized into three groups based on similar characteristics and levels of performance anxiety.
The detail about the organization of the paper is summarized in Fig. 2.
Fig. 2 Organization of the paper.
The clustering process involves dividing the dataset of students’ anxiety N into groups of similar data points, to express the clustering of each student’s anxiety into k clusters. The Euclidean distance^47^ is commonly utilized to quantify and assess the similarity of each student’s anxiety.
Let Ss be the dataset of each student’s anxiety n.
Each sample xi is a point in a d-dimensional space with the anxiety of each student and it can be expressed as.
The objective is to cluster this set into k clusters. The IMOA clustering algorithms aim to group similar samples based on similarity measures. Mathematically, the clustering process can be expressed as.
Equations (3) and (4) divide the student dataset into k clusters, ensuring that none of the clusters is empty. The collection of all clusters forms the sum of Ss, and there are no overlapping samples among the clusters. To evaluate each mayfly, the Davies-Bouldin index (DBI) is adopted, which is a standard method for evaluating potential solutions in cluster analysis^48^. The Ri, j value obtained from this index is then utilized to assess a cluster.
Therefore, this paper aims to minimize the DBI value that indicates the appropriate partitioning of a student dataset.
For the constraints, the problem model is as follows.
The factor Ri can be written
For specific selections of dispersion, distance, and characteristic vectors, the R~ij~ is the function that both meets the necessary conditions and reduces to similarity measures.
Let Si and Sj represent the Euclidean distance within-cluster for the ith and jth clusters, respectively, and mathematically Si can be expressed as
where Ti is the number of individuals in cluster i, Ai represents the centroid of cluster i, q is an integer, Xj is a vector describing those individuals, and the distance between the cluster centers is denoted as Minkowski metric Mij for clusters i and j^49^.
Equation (7) demonstrates that every student anxiety in the dataset is allocated to a cluster based on the least distance and this distance is determined can be obtained using Eq. (8).
where and shows the kth element of vector Ai and it is also the center of cluster i and p = 2 which corresponds to the distance calculated using the Euclidean method.
The mayfly algorithm is a population-based method that depends on motivation from the method that mayflies fly and mate^50^. Most adult males collect in swarms above the water and engage in up-and-down nuptial dance to attract females. To mate with males, females fly into these swarms. From the successful mating, they will give birth to their child and then proceed with their life cycle. For this purpose, a d-dimensional vector x = (x1,., xd) represents potential solutions and randomly moves each mayfly into this space. An objective function f(x) is defined to evaluate the mayflies’ performance. The direction in which a mayfly flies results from a complex interplay between its individual and collective flying experiences and its velocity is represented by the variation in its position (v1, ., vd). Specifically, each mayfly adjusts its sequence to reach two significant targets. Initially, the mayfly endeavors to reach its individual best position (pbest) achieved so far. Then, it aims to approach the best position attained by any mayfly in the entire swarm up to that point (gbest). The male mayfly population is represented by whereas the female mayfly population is denoted by .
It is assumed that represents the current position of mayfly i in the search space at time step t, the position changes by adding a velocity to the current position. The position and velocity of the male mayflies are calculated as follows.
where is velocity of male mayflies i= 1,2,…,n and j = 1,…,n. t is step time, a1 and a2 are the constants, β is the dynamic variable. rp is the distance between Euclidean i mayfly and pbesti. rg is the distance between Euclidean i mayfly and gbesti.
where xij is the jth element of mayfly i and Xi is the pbesti or gbest.
The best position of Mayfly is updated using Eq. (12)
The velocity of the best male mayflies can be calculated as
where f is a function, and d and r are the dance coefficient and random value respectively.
Female mayflies do not gather in swarms as males do. Instead, during the breeding phase, they directly approach the males. To adjust the position of female mayfly i in the search space at time step t, a velocity is added to their current position, denoted as .Similarly, the velocity of the best female mayflies can be calculated as follows.
The best female mayfly is drawn to the best male mayfly, the second-best female mayfly to the second-best male mayfly, and so on. Therefore, their velocity is determined by the following for minimization problems.
where is the velocity of female mayflies j = 1,…,n and i = 1,2,…,M. t is the current iteration, a2 is a constant and β is the fixed factor. fl is the random coefficient, r is a random value and rmf is the distance between both male and female mayflies.
Finally, male and female mayflies engage in mating to produce offspring. As a general principle, the best females are paired with the best males, while the best females are matched with the best males. The selection process can be either random or influenced by their fitness function and the following equations dictate the process of offspring generation.
where λ1 and λ2 are the offspring 1 and 2, η is a random number and m and f are male and female mayflies respectively.
The fundamental MOA encounters several stability issues linked to the velocity disturbance of existing solutions. Additionally, the algorithm exhibits an early convergence characteristic due to an inadequate balance between exploitation and exploration terms^51^. Initially, when r ≥ 2, the value of reached to zero. Currently, possible mayflies cannot be formed since, except for random walk mayflies, the velocity update algorithm for the majority of the population of mayflies does not operate. Secondly, MOA’s convergence speed and global search ability are both negatively affected when the distance between mayflies is ≥ 2, and the modified velocity continues to be ineffective in such a case. Then, a wide range of variable values, the mayflies are relatively far apart at the start of the iteration, s getting close to 0, and the attraction term is ineffective. Mayflies get closer together with each iteration. Finally, the attraction term starts to have an effect and the heuristic for the modified velocity starts to rise gradually when r ≤ 2. At the beginning of the iteration stage, the algorithm’s convergence speed is uncertain, but in the final stages, it moves rapidly. To solve the above problems, the modified velocity for male and female mayflies is obtained using the following Eq.
In the current MOA, the value of β remains constant. A large value of β enhances the algorithm’s exploration capability, while a small value of β strengthens the algorithm’s developmental ability. Consequently, when β is kept as a constant, MOA struggles to optimize the balance between exploration and exploitation. To address this issue, a formula for the adaptive adjustment of β is introduced.
where Maxtime is the maximum running time. runtime is the algorithm run time. rand is a random number between [0,1].
A modified mating operator is also introduced to improve the exploration and explication process in existing MOA. This modification ensures that the offspring mayflies resulting from mating are positioned in proximity to the male mayflies. The explicit mating operators are outlined as follows.
where λ1 and λ2 are the offspring 1 and 2, η1 and η2 are the random numbers, m, and f are male and female mayflies respectively.
The analysis of the algorithm’s time complexity is significant as it serves as a main parameter that highlights the algorithm’s strengths and weaknesses. The time complexity process is presented in Table 1. Assuming a population size of n, with n/2 male mayflies and n/2 female mayflies, and a variable dimension of D, the time complexity analysis is presented in Table 1.
The flowchart and pseudo-code of the proposed algorithm are presented in Fig. 3 and Algorithm 1, respectively. A designated maximum running time, denoted as Maxtime, is established for the algorithm. Once the algorithm reaches the predefined time limit, it concludes its execution and generates the final result.
**** Algorithm 1. Pseudo Code of the IMOA.
Fig. 3 Flowchart of the proposed algorithm.
The bio-inspired optimization algorithms are inherently stochastic, leading to performance fluctuations across multiple runs when generating ideal solutions. As a result, this section demonstrates the effectiveness of the IMOA technique. The developed program was run on an i7 computer operating at 3 GHz with 12 GB of RAM, using MATLAB 2020a for the experiments. Additionally, this section provides a description of the experimental results, their explanation, and the experimental analysis.
The efficiency of the IMOA proves its viability and performance on 23 benchmark functions that are widely utilized and it is mentioned in Table 2. These benchmark functions serve as a standard method to evaluate the efficiency of the optimization technique and they are categorized into unimodal test functions (F1–F7), multimodal test functions (F8–F13), and multimodal test functions with fixed dimensions (F14–F23). Considering the characteristics of the benchmark functions, unimodal test functions (F1–F7) are used to evaluate the algorithms’ exploitation capability, while multimodal test functions (F8–F13) and multimodal test functions with fixed dimensions (F14–F23) are employed to assess their exploration ability. Figure 4a shows the 3D parameter space in a 2D and a detailed analysis of IMOA’s performance across the 23 benchmark functions is presented in the following section.
Fig. 4 Benchmark functions from F1–F23. (a) 2D function plot (b) convergence characteristics (c) box plot representation.
Figure 4b demonstrates the convergence curves obtained using unimodal test functions. Based on the characteristics of the unimodal test functions are employed to verify the algorithms’ exploitation capabilities. As shown in Table 2, IMOA obtained better performance compared to other algorithms across all unimodal test functions, particularly excelling in F4. IMOA not only performs better in unimodal functions but also outperforms other algorithms in both the final test results and convergence rate. The convergence curves of MOA, GWO, MFO, WOA, and IMOA shown in Fig. 4b represent the average values tested across the 23 benchmark functions, each repeated 20 times. It is confirmed from Fig. 4b that IMOA achieves a faster convergence rate in searching for the global optimum. In the unimodal test function evaluations, the convergence rate of algorithms is more crucial than the final results, indicating that IMOA is more stable than MOA, GWO, MFO, and WOA for unimodal test functions.
The ability of an algorithm to escape local optima and locate the global optimum can be evaluated using multimodal functions, as shown in Fig. 4b. When applied to multimodal functions, test results provide a more accurate reflection of this ability than the convergence rate. According to Table 2, IMOA obtained improved results compared to the other algorithms, particularly in F7, F8, F10, and F11. IMOA also achieves a better algorithm in F13. In addition to this WOA shows better results than others in F10, IMOA outperforms MOA, GWO, MFO, and WOA in both the verification results and convergence rate.
Figure 4b illustrates the convergence curves obtained using multimodal functions with fixed dimensions. The capability of an algorithm to escape a few local optima can be evaluated using these functions. As shown in Table 2, IMOA outperforms the other algorithms in F14 to F23, with average performance in F22. However, IMOA performs better than MFO, GWO, and WOA in both the final test results and convergence rate.
Figure 4c shows the boxplot of IMOA compared to other algorithms across 23 benchmark functions. As demonstrated in Fig. 4c, the IMOA algorithm demonstrates better consistency than the other algorithms. The median, maximum, and minimum values for IMOA are more concentrated than those for MOA, GWO, MFO, and WOA. Stability is an important metric for evaluating algorithm performance, reflecting the consistency of results. In addition, standard deviation and box plots effectively estimate algorithm stability by visually representing data variation and providing main statistics elements such as the minimum, second quartile, median, third quartile, and maximum values. Figure 4c also shows the distribution of objective function values for optimal solutions across multiple runs, comparing to IMOA algorithm with others. The results indicate minimal variation in the best solutions obtained from IMOA after > 20 trials, demonstrating its superior stability compared to algorithms like MOA, GWO, MFO, and WOA. Figure 4c shows that IMOA outperforms other algorithms in the box plot results, and shows its improved stability across 23 benchmark functions.
According to Table 2, the evaluation of exploration and exploitation capabilities of the IMOA algorithm using standard test functions is presented. The well-known algorithms are mainly compared through numerical analysis, box plots, and convergence curves. The best, worst, average, standard deviation, rank analysis, and computational time of the obtained results are provided in Table 2. The results obtained using IMOA demonstrate improved average and standard deviation The IMOA algorithm shows a significant advantage in addressing unimodal test function problems, as it achieved the global optimal solution compared to the original MOA and GWO algorithms. In the multi-dimensional test functions (F8–F13), the IMOA algorithm achieves better simulation results than the other algorithms. Particularly, for functions F11 and F12, IMOA achieves the ideal optimal value. The results for both unimodal and multimodal functions indicate that IMOA has superior performance in terms of exploitation and exploration capabilities, with a higher possibility of escaping local optima. This demonstrates that the introduced improvement strategy effectively enhances the balance between exploration and exploitation within the IMOA algorithm. The IMOA is based on a dynamic variable mechanism, which facilitates stable exploration and development capabilities, allowing for easy escape from local optima. For the fixed-dimension benchmark functions (F14–F23), the IMOA algorithm obtains better solutions with smaller deviations. Specifically, for functions F18 and F19–F21, IMOA achieves the theoretically optimal average and standard deviation. The lower standard deviation indicates that IMOA exhibits better stability, ensuring more accurate results during application. The results from the fixed-dimension test functions illustrate that the proposed IMOA maintains a better balance between exploration and exploitation due to the combination of the dynamic variable. Table 2 presents the average computation time for each algorithm, along with the total running time for all algorithms, with IMOA ranking 1st in most of the benchmark functions. This confirms that the IMOA algorithm requires less time than the other original algorithms.
The original number of individuals in this dataset is 1001 however, for this work, they are considered as 1000. According to Table 3 in the first test case, the analysis focuses on mathematics score performance, examining how well students understand and apply mathematical concepts under exam conditions. This includes evaluating problem-solving skills, accuracy, and time management. In the second test case, the focus shifts to reading score assessment, where performance is gauged by the student’s ability to comprehend, interpret, and analyze written text, with an emphasis on critical reading skills and comprehension efficiency. The third test case analyzes writing scores, assessing the student’s ability to structure their thoughts, develop coherent arguments, and convey ideas clearly, focusing on grammar, vocabulary, and overall writing proficiency. Table 3 shows the descriptive analysis of student emotions test cases and provides insights into the central tendency, variability, and distribution of emotions experienced by students. These statistical measures help teachers to understand the emotional landscape of students and classify patterns in their emotional responses. Furthermore, the higher values indicate more negative emotional states.
The study aims to classify students’ physiological levels by using IMOAs. Both qualitative and quantitative assessments are used to evaluate the dynamic performance of the problem model as mentioned in Eq. (5). The study focuses on analyzing key performance factors, such as population size and the number of iterations. All optimization techniques undergo analysis under the same initial conditions, boundary limits, and problem constraints. In this research work, initially, a dataset comprising anxiety data from 1000 students, with 52% males and 48% females sharing similar feelings, is collected. Secondly, the IMOA algorithm is employed to categorize the anxiety data into Clusters A and Cluster B. Finally, a statistical analysis is conducted using SPSS and Jamovi, enabling educators and mental health professionals to better support students through clustering.
This type of emotion scale focuses on the importance of mathematics score performance and anxiety, examining how well students understand and apply mathematical concepts under exam conditions. By exploring the relationship between anxiety and performance, the study aims to identify how stress impacts students’ ability to effectively solve mathematical problems during tests. Understanding this connection can help in developing strategies to reduce anxiety, improve mathematical comprehension, and ultimately enhance academic performance. To demonstrate the effectiveness of the proposed IMOA algorithm in comparison to the MOA, MFO, GWO, and WOA algorithms, average values of 74.3 and 50.2 are considered for clusters 1 and 2, respectively. To explore the efficiency of IMOA, the test results are compared with other algorithms, as presented in Fig. 5. According to Fig. 5a, it is confirmed that 26.8% of individuals are contained in cluster B, while 73.2% are in cluster A.
Fig. 5 Graphical presentation of clusters. (a) IMOA (b) MOA (c) MFO (d) GWO (e)WOA.
In this case, the reading score assessment lies in evaluating a student’s ability to comprehend, interpret, and analyze written text. This analysis focuses on critical reading skills, comprehension efficiency, and the ability to extract meaning from complex information. By examining reading performance, educators can identify strengths and areas for improvement, ultimately helping to develop targeted interventions to boost literacy skills. Strong reading abilities are fundamental for academic success across all subjects, making this assessment a key indicator of a student’s overall learning capability and future academic potential. To evaluate the efficiency of the proposed method, a test case involving assessment during the examination is analyzed. After conducting > 20 trials, the IMOA method achieved the best solutions, with an average value of 76.7 for cluster 1 and 53.1 for cluster 2. The results show that the proposed IMOA method performs better in classifying student anxiety levels. Figure 5 presents the cluster analyses obtained using the IMOA, MOA, MFO, GWO, and WOA algorithms, respectively.
The importance of analyzing writing scores is in assessing a student’s ability to structure and express their thoughts clearly. This evaluation focuses on coherence, organization, grammar, and clarity in communication. Examining writing performance identifies students’ ability to present ideas and arguments effectively, which is crucial for academic success across subjects. The analysis helps educators improve students’ writing and overall communication skills. In this case, by focusing on writing scores related to test results, the effectiveness of the proposed IMOA method is verified, as shown in Fig. 5. To validate its superiority, the results obtained from IMOA are compared with other algorithms. The lowest average values over more than 20 trials for various methods are 75.9 and 50.7, respectively, showing that the IMOA method consistently generates lower average values compared to MOA and other methods. This suggests that the performance of the proposed method is better, particularly when compared with WOA. Figure 5 shows the individuals obtained for different test cases related to student anxiety. The comparison of results indicates that the IMOA method has better results due to its exploration and exploitation capabilities.
In this research work, two clusters are analyzed based on three attributes. The Euclidean distance measures the similarity between data points and cluster centroids, indicating that students closer to a centroid are more likely to belong to that cluster. In Fig. 5, each small circle represents an individual student assigned to either Cluster A or Cluster B. However, each dataset is limited to belonging to only one cluster, ensuring distinct boundaries between clusters that do not overlap, allowing the dataset to be accurately grouped into either Cluster A or Cluster B. According to Fig. 5a, the IMOA effectively classifies student data points with homogeneous characteristics into Clusters A and B, achieving lower average values. The graphical representation produced by IMOA allows for an effective exploration of the results for both clusters. In test cases 1, 2, and 3, Cluster A has a population distribution of 732, indicating that the clusters are well separated. Figure 5b shows the obtained result from the MOA, where the dataset is divided into clusters A and B, with populations of 678 and 322, respectively, across all three test cases. Figure 5c illustrates the results from the MFO, which shows the same clustering pattern, with Cluster A containing 690 data points and Cluster B containing 310 data points. Additionally, Fig. 5d shows that the GWO produced datasets of 601 and 399 data points for Clusters A and B, respectively. Figure 5e shows that the WOA resulted in dataset sizes of 682 and 318 for both clusters. However, IMOA consistently shows better performance in classifying and compact clusters across various configurations, as confirmed by graphical representations that confirm its optimal performance and balanced distribution of data points within the clusters.
Table 4 shows the performance of the IMOA algorithm, highlighting its performance as compared to competent algorithms. The obtained results are further verified using analysis. IMOA consistently achieved the lowest average value in test cases 1 and test case 2, demonstrating its performance than other algorithms and securing the top rank. Additionally, comparisons with other algorithms further validate these results, showing that IMOA not only required less computational time but also demonstrated greater accuracy. These findings confirm the robustness of IMOA in classifying psychological problems based on attributes, positioning it as a superior method compared to existing techniques.
According to Table 4, students in Cluster A achieve the highest scores across all test cases, while students in Cluster B tend to have average or lower values. The average values achieved by IMOA, MOA, MFO, GWO, and WOA for test case 1, in cluster A, were 74.3%, 75.4%, 75.2%, 77.0%, and 75.4%, respectively. In cluster B, IMOA achieved an average of 50.2%, while MOA, MFO, GWO, and WOA scored 51.7%, 51.3%, 53.9%, and 51.6%, respectively. Although MFO outperformed GWO in cluster A, IMOA demonstrated the best overall performance. Therefore, IMOA showed better results than other techniques. In test case 2, IMOA achieved an average value of 76.7% in cluster A, while MOA, MFO, GWO, and WOA scored 77.8%, 77.5%, 79.2%, and 77.7%, respectively. IMOA’s lower average value, particularly compared to GWO and WOA, demonstrates its effectiveness in generating more precise and compressed clusters. In cluster B, IMOA achieved 53.1%, with MOA, MFO, GWO, and WOA scoring 54.9%, 54.5%, 57.0%, and 54.8%, respectively. In test case 3, the average values in cluster A were 75.9% for IMOA, 77.0% for MOA, 76.7% for GWO, and 78.6% for WOA. These results show that IMOA, MOA, GWO, MFO, and WOA performed well, but IMOA consistently shows better performance in the classification of student clusters across different test cases. In cluster B of test case 3, the average values are 50.7% for IMOA, 52.6% for MOA, 52.3% for GWO, 54.9% for MFO, and 52.5% for WOA. IMOA significantly outperformed both MFO and WOA, demonstrating its effectiveness in solving the classification problem.
The graphical representations in Fig. 5 demonstrate the classification and monitoring of psychological problems, showing how student data is grouped within Cluster A and Cluster B. These visuals assist researchers in evaluating cluster consistency and separation, ensuring appropriate cluster selection and quality. According to Table 4, IMOA consistently achieved the lowest average value across clusters and test cases, outperforming MOA, GWO, MFO, and WOA. This analysis confirms IMOA’s superior performance in the classification of psychological problems. According to the obtained results, IMOA demonstrates better performance in classifying anxiety problems due to different key enhancements. First, the optimization of the DBI allows for a robust assessment of cluster quality, measuring both inter-cluster separation and intra-cluster cohesion. This ensures that clusters are not only distinct from one another but also internally cohesive, enhancing classification effectiveness. Second, IMOA is based on a dynamic parameter that improves its velocity relative to the original MOA. This velocity enhancement makes IMOA particularly effective in addressing the complexities of classifying student psychological issues. Then, the algorithm maintains a well-balanced approach to exploration and exploitation, allowing it to navigate the solution space thoroughly. This balance facilitates the discovery of diverse cluster configurations while refining existing solutions for better accuracy. Furthermore, IMOA demonstrates better performance in datasets where each student data point must be assigned to a single cluster. This careful handling of limitations enhances the clarity and accuracy of classifications. Additionally, IMOA shows better convergence properties compared to other algorithms, enabling faster and more reliable classification of psychological issues among students. Finally, these improvements contribute to high consistency and reliability in clustering results, emphasizing IMOA’s effectiveness in classification problems.
The dataset used in this research was obtained from Kaggle and provides information on student’s mathematical performance as well as demographic details, such as gender, race/ethnicity, lunch status, and completion of test preparation courses. In this research, performance is analyzed using standardized test scores in mathematics, reading, and writing.
For example, students coming from low-income families may worry about their math scores. Despite their hard work, they may struggle to keep up with their classmates who may have access to extra test preparation courses. This highlights the significant impact of parental education and economic background on the academic performance of students, who may struggle with anxiety considering their school performance, which can further affect their performance in a negative way. In this research, three key attributes like math score, reading score, and writing score are used to classify students based on their concerns or anxieties about these scores. This classification process groups students based on their worries about their performance in these subjects, facilitating the identification of groups with similar levels of concern.
Another example is students having better performance in reading and writing but struggling with mathematics. They may feel isolated and anxious, believing that their future opportunities depend heavily on their math performance. Through psychological clustering, they can be identified as part of a group struggling with social anxiety^52^. This allows the Education Institute to implement targeted support, such as social skills workshops and peer mentoring programs. Over time, students are expected to begin feeling more connected and less anxious, leading to improved academic performance and overall well-being.
By employing IMOA, this study categorizes students into clusters based on their anxiety about math, reading, and writing scores. This enables educators and mental health professionals to provide more targeted support. Identifying specific clusters allows schools to implement interventions such as academic support or counseling. After the clustering process, further analysis can show how such interventions create a more inclusive and supportive environment. Students who may struggle with isolation can receive the attention and resources they need, improving individual outcomes and fostering a sense of community and belonging within the school. The proposed method serves as a valuable tool for investigating how various factors affect high school students performance in math, reading, and writing. The classification of students based on their academic worries using IMOA provides insights that could help in creating interventions and support strategies for different student clusters. By identifying the clusters of students who are most concerned about their academic performance, this research contributes to improving educational outcomes and promoting student well-being. Additionally, psychological clustering can help to validate mental health issues. By addressing different emotional and psychological needs, schools can promote a culture of empathy and understanding. Students learn that seeking help is acceptable and that they are not alone in their struggles.
In this research, the classification of students’ psychological problems is explored using IMOA. However, there is still to expand its applications to practical uses in various fields, such as engineering and biomedicine, while also utilizing its flexibility and maximizing its potential impact. According to the obtained results, IMOA demonstrates better performance and efficiency in classification. Furthermore, IMOA shows improved performance and results in various applications. These obtained results further demonstrate the significance of IMOA as an effective technique and motivate further research across different fields.
The objective of this study is to classify student anxiety levels using the IMOA algorithm. The obtained results show that IMOA can provide better solutions to the NP-hard problem of making student clusters based on homogeneous characteristics of anxiety. Initially, a dynamic variable is introduced to further improve the performance of MOA, specifically, their failure to update the velocities of certain mayflies when there is a considerable distance between them. The enhanced velocity does not impose limits on modifying the velocity and position of an individual during iteration, even when there is a large distance between individuals. The IMOA proposed adjusting the dynamic factor, enabling strong global search abilities in the initial phase and robust local search abilities in the final phase. Furthermore, an improved mating operator is presented to enhance the probability of generating better candidate solutions during the mayfly mating process. The IMOA demonstrates enhanced solution quality and better convergence, as observed in its performance across 23 benchmark functions evaluating exploration and exploitation. Moreover, statistical analysis further confirms the efficiency of IMOA. According to the obtained results, IMOA achieved the lowest average values for test case 1, with 74.3% for cluster 1 and 50.2% for cluster 2. In test case 2, the average values of 76.7% for cluster 1 and 53.1% for cluster 2 are obtained. In test case 3, IMOA obtained average values of 75.9% and 50.7%. When compared to other algorithms such as GWO, MFO, WOA, and MOA, the IMOA method performs well, highlighting better classification abilities and smooth convergence to optimal solutions.
The objective of this study is to classify student anxiety levels using the IMOA. However, there are certain limitations. Specifically, understanding its performance on larger-scale problems and its efficiency with different types of functions can help identify areas for enhancement and improve its application. Initially, it is highly sensitive to parameter settings, which may lead to average results if not properly configured. Secondly, the IMOA may struggle to escape local optima in complex problems, restricting its effectiveness in identifying global solutions. Finally, the algorithm faces challenges in exploring large search spaces, which can reduce its ability to discover diverse solutions. These limitations, along with the success of IMOA in this research work, highlight the need for further research and enhancements to improve its performance. Future research should focus on scalability, computational complexity, parameter sensitivity, and its application to non-linear, multi-objective, and dynamic optimization scenarios. To address these limitations, the following are a few future directions that should be considered.
The authors are grateful for the support of the work by the Research Grant Scheme, Hanshan Normal University, Guangdong, China. The authors also thank the anonymous reviewers for their constructive advice.
Methodology, M.S.S., and X.D. software, M.S.S.; writing—original draft preparation, M.S.S.; writing—review and editing, X.D., C.W. and G.Z.; visualization, C.W. and Z.K.; supervision, X.D.; project administration, X.D., and G.Z.; All authors have read and agreed to the published version of the manuscript.
This work is supported by the innovation teams of ordinary Universities in Guangdong Province (2021KCXTD038, 2023KCXTD022), Key Laboratory of Ordinary Universities in Guangdong Province (2022KSYS003), China University Industry, University, and Research Innovation Fund Project (2022XF058), Key Discipline Research Ability Improvement Project of Guangdong Province (2021ZDJS043, 2022ZDJS068), Special Projects in Key Fields of Ordinary Universities in Guangdong Province (2022ZDZX3011, 2023ZDZX2038), Chaozhou Engineering Technology Research Center, Chaozhou Science and Technology Plan Project (202102GY17, 202201GY01), and the Quality Engineering Project of Hanshan Normal University (HSJYS-KC22719).
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
The authors declare no competing interests.
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.